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Local indicability in the presence of diagrammatic reducibility

2025/11/19 by Harlander, Jens, Rosebrock, Stephan
Computer Science · Mathematics · #20F05 #20F06 #20F65 #57M05 #57M07 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · doi:10.48550/arxiv.2511.15212

openalex publication_date 2025/11/19 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/28

Abstract

If a complex X is a subcomplex of a diagrammatically reducible 2-complex Y that has locally indicable fundamental group, then X has locally indicable fundamental group. This is a consequence of the Corson-Trace characterization of diagrammatic reducibility. In this paper we use a Corson-Trace like characterization of diagrammatic reducibility away from a subcomplex to obtain a considerable stronger result. We apply this to the question of local indicability in the context of Whitehead's asphericity conjecture. We show that an injective labeled oriented tree (LOT) that is diagrammatically reducible of degree 2, and all its quotients are as well, is locally indicable.

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